Preheat oven to 425°F. Sprinkle chicken thighs evenly with pepper and 1 teaspoon salt. Place chicken, skin sides down, in a large cast-iron skillet. Cook, over medium, until fat is rendered and skin is crispy, 10 to 15 minutes. Flip chicken, and cook until browned but not cooked through, about 2 minutes. Transfer chicken to a large plate, reserving drippings in skillet.

While chicken browns, toss broccolini with oil and ¼ teaspoon salt; arrange in an even layer on a large rimmed baking sheet. Bake until broccolini is tender and charred in spots, about 12 minutes. Reduce oven temperature to 350°F. Cut broccolini into ¾-inch pieces; set aside.

Add shallots and garlic to drippings in skillet; cook over medium, stirring constantly, until fragrant, about 1 minute. Add orzo; cook, stirring constantly, until starting to brown, about 1 minute. Add chicken broth and remaining ¼ teaspoon salt; bring to a simmer over medium. Remove from heat, and nestle reserved chicken and any accumulated juices in skillet.

Bake at 350°F, uncovered, until orzo is al dente and a thermometer inserted into thickest portion of the chicken registers 170°F, 12 to 15 minutes.

Remove skillet from oven; transfer chicken to a plate, and let rest. Stir cheese, thyme, lemon zest, and reserved broccolini mixture into orzo until creamy and smooth.

Garnish with additional thyme leaves, and serve with chicken.